Efficient algorithm for counting unique states of tic tac toe

I'm trying to build a tic tac toe game to demonstrate and experiment with machine learning algorithms, and i've found an interesting problem.

eg: a tic tac toe board can be mirrored, but for a machine learning purposes both these states are equivilent

x _ o     o _ x
o o x  =  x o o
_ _ _     _ _ _

like-wise rotations

x _ o   _ _ x   _ _ _   o _ _
_ _ _ = _ _ _ = _ _ _ = _ _ _ 
_ _ _   _ _ o   o _ x   x _ _

finally, juxtapositions

x _ o   o _ x
_ x _ = _ o _
_ _ x   _ _ o

what is the best way to identify/count the unique states for tic tac toe?

is there a field of study or mathematics that I should look into ?